Talk:Heptomino

The diagram at top right of the page has an error in that tiles 6.11 and 7.9 are the same. (Counting down and across.)

One should be replaced by the tile that looks like this:

 X
 XX
XX
X
X

In other words tile 7.9 could be altered by sliding the single square to the right up one place.

Frankd48 (talk) 05:26, 18 April 2009 (UTC)[reply]

Done --ἀνυπόδητος (talk) 18:18, 27 October 2009 (UTC)[reply]

Tiling the plane

This question regards multiple polymino articles. Does the statement "All but four heptominoes are capable of tiling the plane" mean that they tile it individually or in combination with other heptominoes? Moberg (talk) 13:44, 16 July 2011 (UTC)[reply]

Yes, individually. Given almost any one heptomino, it is possible to tile the entire plane with copies of that one single heptomino -- unless it is one of those four heptominoes.

How can we make this less ambiguous, to comply with WP:OBVIOUS ? --DavidCary (talk) 15:01, 8 January 2014 (UTC)[reply]

Problem

The article says:

Although a complete set of 108 heptominoes has a total of 756 squares, it is not possible to pack them into a rectangle. The proof of this is trivial, since there is one heptomino which has a hole.^[1] It is also impossible to pack them into a 757-square rectangle with a one-square hole because 757 is a prime number.

All but four heptominoes are capable of tiling the plane; the one with a hole is one such example.^[2]

Using a new term, regular polyomino meaning a polyomino without a hole, can we pack all regular heptominos into a rectangle?? Georgia guy (talk) 19:47, 2 February 2012 (UTC)[reply]

Only if they can be packed into a 7x107 rectangle, as 7 and 107 are primes. I can't think of a definitive answer at the moment. --ἀνυπόδητος (talk) 20:06, 2 February 2012 (UTC)[reply]

regular polyominoes are called simply connected. Yes, it is possible to pack 107 simply connected heptominoes into the rectangle 7x107. It is also possible to pack all 108 heptominoes into three rectangles 11x23, each of them containing hole 1x1 in the center (see also Golomb's 1965 book Polyominoes). --Stannic (talk) 05:27, 13 August 2013 (UTC)[reply]

References

^ Grünbaum, Branko (1987). Tilings and Patterns. New York: W. H. Freeman and Company. ISBN 0-7167-1193-1. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
^ Gardner, Martin (1965). "Thoughts on the task of communication with intelligent organisms on other worlds". Scientific American. 213 (2): 96–100. {{cite journal}}: Unknown parameter |month= ignored (help)

[Gruenbaum-1] Grünbaum, Branko (1987). Tilings and Patterns. New York: W. H. Freeman and Company. ISBN 0-7167-1193-1. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

[2] Gardner, Martin (1965). "Thoughts on the task of communication with intelligent organisms on other worlds". Scientific American. 213 (2): 96–100. {{cite journal}}: Unknown parameter |month= ignored (help)

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